Numerical analysis of the spectrum for the highly oscillatory integral equation with weak singularity
Gao, Jing1
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作者信息
1. Xi An Jiao Tong Univ
折叠
Abstract
In this paper, we focus on the spectra numerical computation for the integral equation with the absolute oscillation and power-law or logarithmic singularity. Finite section method is applied to transform the integral equation to an algebraic eigenvalue problem. The entries of the coefficient matrix appearing in the bivariate highly oscillatory singular integrals can be represented explicitly in Gamma or the exponential integral functions. The decay rate of the entries is established to construct the truncation scheme. Then the infinite algebraic eigenvalue problem can be simplified to be the finite one. The corresponding error of the infinite and finite algebraic systems is also bounded. Finally, the numerical experiments are provided to illustrate the theoretical analysis. (c) 2021 Elsevier B.V. All rights reserved.
Key words
Oscillatory singular integral equation/The modified Fourier basis/Spectra problem/Asymptotic order/Pseudo-spectra/QUADRATURE/APPROXIMATION/COMPUTATION
NSTL
Elsevier